To everyone saying it keeps things cold - you're wrong. A computer that idles at 45C on air cooling, will be at 80C in the oil - not at first, but the specific heat is higher.
In order for the oil to stay cool, you need some sort of radiator or exhaust fan to cool the oil - this could damage any sort of radiator-like equipment. Notice I said "could," not "will."
Is there anything good with submerging your computer in mineral oil? Sounds weird to me
Goods: unlike closed water cooling that can spring leaks, you're creating one big leak here
So the good is that it won't damage your components initially. Over time they may become contaminated with conductor and semi-conductor materials, possibly causing your board to short or hang. Though due to the properties of the oil, this is less likely to occur.
Other benefit is that it is neat; you can make light shows, bubbles, or other interesting affects with this.
If you manage to hook up an intense radiator, it will keep your computer cool, theoretically, possibly cooler than H2O cooling, due to the fact that all the board is touching the oil - the cooling depends on how well the oil is circulated, cooled, and then re-ented back in the tank.
I would think it is pretty useless and why would you need to keep the fan if it is submerged in the oil?
The fan acts like a fountain in the middle of a lake, it's not there to look at (just for aesthetic value), it's there to move the algae. In the computer's case, it's there to move/circulate the oil to help cool it down, or at least disperse the hot oil and hopefully have it replaced by cooler oil.
A high CFM fan should have enough juice to continue to move in the liquid. I would like to note that while this slows down the heat rise, it does not prevent it. In fact, it barely would even cool the case, but it does help to prevent any semi-conductor/conductor material that is lost to the oil, to short the board.